I think it will safe, sustained, efficient nuclear fusion.
You?
I’d love it to be fusion, but it’ll probably be nanotech and genetic engineering - you know, the little stuff.
The wheel, the plow, and the hut.
Wait, is this before or after the nuclear war?
Lol, well played.
Easily it will be abundant, cheap carbon free energy and the logistics to support it on a massive scale. My guess is it will be a nuclear/hydrogen combination for personal transport, with baby pebble bed nuclear reactors springing up all over the place and a hydrogen infrastructure and price that makes it nearly transparent to switch over (maybe some government incentives to trade in your hydrocarbon burning vehicle for something that runs cleaner, maybe some way to replace the chassis completely with a fully built hydrogen chassis for half the price of a new car…something like that).
-XT
Nanotech and genetic engineering seconded.
While I think that abundant cheap power will turn up and be highly significant, from the point of view of mankind I reckon that genetic engineering of humans will be the most significant development.
A switch away from fossil fuels. The commercialisation of space - perhaps an orbital tower will be started.
I think there’s still a good bit of interesting development left to squeeze out of materials development - photovoltaic, electromechanical and electroluminescent fabrics, superstrong ceramics, artificial diamond semiconductor substrates, new semiconductor materials - stuff like that.
Oh, and flying cars, they’ll be ready any day now.
My vote is for something-we-can’t-even-imagine-yet. After all, who in 1957 would have even imagined The Straight Dope?
I think it will be more along the lines of computing power so pervasive that it will change the way we live. I am not sure what form this will take, but fiction is full of possibilities.
My favourite is enhanced awareness. We will all have language translation, telephone, GPS and Google (or whatever form searching takes then) accessible without the need to look at a little handheld screen.
Dream of Snow Crash dystopias at your own peril
Seconded.
Oh sure, all the other things will happen too, but the big one will be unpredictable. At least I hope so.
And regarding The Straight Dope, it will evolve into The Planar Dope, The Cubic Dope, The Temporal Dope, etc.
Thirded. It will be something we’ve never thought of before.
You mean perhaps a wristwatch that teaches you how to use its memory, computing power and communications - a very real possibility.
However I don’t think that Borgism/Droidism will be the most significant development - imagine an injection that doubles your IQ (or even repairs lost synapses due to alcohol consumption).
I think the gravistatic emolufier will be be quite widely used, and every home will be equipped with at least one chronoflourescent morphosymmetricator.
Neuro-computer interfaces.
Seconded. If they perfect that, what you’ve got is mechanically assisted telepathy.
You mis-spelt ‘telephony’ 
An increase in battery storage capability by many orders of magnitude.
If the interface is direct-to-brain and doesn’t involve the auditory functions, ‘telephony’ would not be an appropriate term.